asymptotic granularity reduction and its application
文献类型：期刊论文
| 作者 | Su Shenghui ; L&# ; Shuwang ; Fan Xiubin |
| 刊名 | Theoretical Computer Science
 |
| 出版日期 | 2011 |
| 卷号 | 412期号:39页码:5374-5386 |
| 关键词 | Algebra Asymptotic analysis Public key cryptography |
| ISSN号 | 3043975 |
| 英文摘要 | It is well known that the inverse function of y=x with the derivative y′=1 is x=y, the inverse function of y=c with the derivative y′=0 is nonexistent, and so on. Hence, on the assumption that the noninvertibility of the univariate increasing function y=f(x) with x>0 is in direct proportion to the growth rate reflected by its derivative, the authors put forward a method of comparing difficulties in inverting two functions on a continuous or discrete interval called asymptotic granularity reduction (AGR) which integrates asymptotic analysis with logarithmic granularities, and is an extension and a complement to polynomial time (Turing) reduction (PTR). Prove by AGR that inverting y≡xx(modp) is computationally harder than inverting y≡gx(modp), and inverting y≡gxn(modp) is computationally equivalent to inverting y≡gx(modp), which are compatible with the results from PTR. Besides, apply AGR to the comparison of inverting y≡xn(modp) with y≡gx(modp), y≡gg1x(modp) with y≡gx(modp), and y≡xn+x+1(modp) with y≡xn(modp) in difficulty, and observe that the results are consistent with existing facts, which further illustrates that AGR is suitable for comparison of inversion problems in difficulty. Last, prove by AGR that inverting y≡xngx(modp) is computationally equivalent to inverting y≡gx(modp) when PTR cannot be utilized expediently. AGR with the assumption partitions the complexities of problems more detailedly, and finds out some new evidence for the security of cryptosystems. © 2011 Elsevier B.V. All rights reserved. |
| 收录类别 | EI |
| 语种 | 英语 |
| WOS记录号 | WOS:000294592500022 |
| 公开日期 | 2011-10-10 |
| 源URL | [http://124.16.136.157/handle/311060/14063]  |
| 专题 | 软件研究所_软件所图书馆_期刊论文 |
| 推荐引用方式 GB/T 7714 | Su Shenghui,L&#,Shuwang,et al. asymptotic granularity reduction and its application[J]. Theoretical Computer Science,2011,412(39):5374-5386. |
| APA | Su Shenghui,L&#,Shuwang,&Fan Xiubin.(2011).asymptotic granularity reduction and its application.Theoretical Computer Science,412(39),5374-5386. |
| MLA | Su Shenghui,et al."asymptotic granularity reduction and its application".Theoretical Computer Science 412.39(2011):5374-5386. |
入库方式： OAI收割
来源：软件研究所
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